A method and a compact gas discharge tube of this kind are known from e.g., European Patent Application No. 84113977.7. In the case of this known discharge tube, or envelope, the ends of those limbs in which no electrode is fitted are sealed off prior to effecting the connection or juncture between the two U-shaped main components. This connection is effected in a manner similar to that described in British Patent Application No. 2 048 562 A, i.e. the tube wall is heated in the proximity of the end of the limb of one main component, so as to soften the glass, after which a tubular collar is blown out from the glass wall, perpendicularly thereto. A corresponding collar is then produced on the other main component of the discharge chamber in a similar manner, and the two collars are joined together by applying heat thereto, so as to form a short, narrow connecting tube. Although this known method may appear attractive from the aspect of manufacture, it has been found to have several drawbacks. For instance, the glass is not uniformly distributed during the glass softening stage of the process, thereby giving rise to stress concentrations and to the risk of fracture. Furthermore, the narrow connecting tube is liable to crack, both during manufacture and during use. A substantial risk of such a failure occurs when fitting the discharge tube, or envelope, onto its lamp fittings. The quality of the discharge tube is also impaired by the fact that the cross-sectional area of the connecting tube is much smaller than the cross-sectional area of the remainder of the discharge tube, which has a negative effect on the light emittin g properties of the discharge tube. This is due to the fact that every constriction in the path of the gas discharge results in an increase in the total operating voltage and therewith in greater losses in the discharge path. Since this increase in losses does not result in a corresponding increase in light flux, it will only impair the efficiency of the discharge tube. Moreover, the presence of constrictions in the discharge path results in a higher striking voltage, or starting voltage, which negatively effects the willingness of the discharge tube to ignite at low temperatures. In addition, the necessary cold zones are only produced at the outer end of the lamp incorporating such a discharge tube, which represents a disadvantage, since the gas discharge lamps must be capable of functioning irrespective of their orientation. For example, the temperature at which the optimal mercury vapour pressure is engendered may prevail at the location where the discharge tube is connected to the lamp base.